Several reasons. First and foremost, if made properly, the Mini is a sealed vessel, meaning the only oxygen getting to the fire is what you give it through your settings on the vents. The ECB has an open bottom with a predetermined gap around the coal pan which provides a constant flow of air. If it's windy and/or cold, the amount of oxygen to the fire remains the same (or changes arbitrarily) so the pit temperature reacts. With the mini, you can adjust the vents according to external conditions so if you're shooting for 250˚ let's say, and the wind picks up, you can adjust the air getting to the coals to raise or lower the "flame" so you can maintain that 250˚
Secondly, the ECB has one of several versions of a coal pan, some with holes in it, some without. This is an inherently difficult way to maintain a charcoal fire. The fire, once again, gets and uses whatever oxygen is available, and the ashes have nowhere to go. Thus, burn times suffer. The mini utilizes (depending on the builder) one form or another of a charcoal basket. The fire easily utilizes the available oxygen from all sides and the ashes fall away. The coals burn more efficiently allowing for more controlled and longer burns. Think of it this way. Let's say you have 2 burners on your stove. One is a regular burner, with a knob that adjusts the flame or coil from low to high. The other simply has an on and off switch. Burner A allows you to boil water, simmer stew, stir a custard and everything in between. Burner B only offers you one level of heat, so if you want to do anything that requires a different level of heat, you have to move your pot on and off the burner to maintain whatever temp you're going for. Which one would you use?
Lastly, the ECB uses a water pan. Granted this is easily worked around, but the guy who goes to the hardware store, buys an ECB, reads the instructions and sets out to smoke meat is probably going to use water in the pan. Again, this is an inherently difficult way to go. As a concept, a gallon or so of water as a heat sink is a good idea. However, in practice, not so much. Water evaporates, meaning your heat sink is diminishing from the time it hits the heat. In a perfectly controlled laboratory experiment the water would evaporate at the exact same rate as the coals burn down, meaning the amount of water needed to regulate the fire remains in perfect harmony with the size of the fire, leading to the last drop of water evaporating at the exact instant the fire burns out. Ummm, yeah right. This ain't gonna happen. What is going to happen is that the operator of the ECB is going to have a couple beers, get distracted by the game or his guests and not realize that the water has cooked away. By the time he checks on his smoker, it's at 500˚ and his dinner is toast. If he does notice the temp spiking before his food is destroyed, he's going to try and refill the water pan, resulting in a cloud of extremely hot steam burning his hand, causing a violent reaction of the aforementioned hand resulting in the better part of a gallon of water being dumped into the coal pan, extinguishing the fire, creating more hot steam and coating dinner with a layer of ash. The mini uses a solid mass of ceramic, sand, iron or stone as a heat sink. This remains constant, thus allowing the operator to adjust the fire to maintain whatever level of heat he wants. Again, which would you choose?
**These assertions are the result of my own personal experience. The ECB is a fine cooker, I just happen to prefer the Mini for my use. Your experience will dictate which is right for you.